The human cerebellum has almost 80% of the surface area of the neocortex

Significance The cerebellum has long been recognized as a partner of the cerebral cortex, and both have expanded greatly in human evolution. The thin cerebellar cortex is even more tightly folded than the cerebral cortex. By scanning a human cerebellum specimen at ultra-high magnetic fields, we were able to computationally reconstruct its surface down to the level of the smallest folds, revealing that the cerebellar cortex has almost 80% of the surface area of the cerebral cortex. By performing the same procedure on a monkey brain, we found that the surface area of the human cerebellum has expanded even more than that of the human cerebral cortex, suggesting a role in characteristically human behaviors, such as toolmaking and language.


Materials and Methods
Specimen preparation and scan parameters. Cortical surface reconstruction methods developed for in vivo MRI images (1) were adapted to reconstruct the cortex of a formalin-fixed human cerebellum (62 year old female, cerebellum width: 96 mm, obtained post-mortem, deidentified prior to use in this study). The specimen was placed in a Fomblin-filled sealed acrylic cylinder, pressurized to approximately twice atmospheric pressure, and refrigerated and vibrated to induce air bubbles to dissolve. The sample was depressurized and warmed to room temperature several hours before scanning. The cylinder fit snugly within a 6 cm inside diameter quadrature RF coil, which was tuned with the sample in place using an RF analyzer. It was scanned on a 9.4T MR scanner (Agilent Technologies, Santa Clara, CA, USA) with short and long echo time (TE) standard 3D gradient echo (FLASH) sequences (9.4T; proton-density weighted (PD): flip=10deg, TE=3.7ms, TR=15ms; effective transverse relaxation time-weighted (T2*): flip=20deg, TE=18ms, TR=30ms; both scan sets used matrix: 512 x 340 x 340; isotropic 0.19 x 0.19 x 0.19 mm voxels; NEX=10; total time: 12h). Gray/white contrast was excellent in the T2* image and somewhat reduced in the PD image. Contrast between the granule cell and molecular layers of the cerebellar cortex in the T2* image varied somewhat across regions but was uniformly non-existent in the PD image. Since the bandwidth for both scan types was equivalent, B0-induced image distortion will be the same in both image sets. Our voxel width was roughly one-half the width of the long axis of the planar dendritic fields of human Purkinje cells.
Surface reconstruction. We updated the original FreeSurfer surface-reconstruction software utilities (1) to allow native use of 512 3 data sets (nominally 0.5 x 0.5 x 0.5 mm, but see below), improved anisotropic filtering, and adequate performance with much denser tessellations (free downloads of csurf for macOS 10.6.8 and higher, and linux CentOS 5.9 and higher are available at https://mri.sdsu.edu/sereno/csurf or http://www.cogsci.ucsd.edu/~sereno/.tmp/dist/csurf). The 5 cerebellum was reconstructed as a single closed surface without dividing it into left and right hemispheres.
Raw averaged T2* and PD images (Fig. 1, top row) were first masked to zero the nearlyzero Fomblin signal outside the sample. We then brightness-normalized the T2* image by dividing it by the PD image, further flattened the result with AFNI 3dUniformize, and then brightness-inverted it so that white matter was lighter than gray matter, while keeping the region outside the cerebellum black (brain.mgz).
The final combined data set was then imported into csurf (but without downsampling it to 0.5 mm wide voxels, so no resolution was lost) and then anisotropically filtered: for a 7x7x7 voxel volume around each voxel, the plane of least brightness variation (perpendicular to one of 21 icosahedral search axes) was found, and then a 2D Gaussian was applied just in that plane (with a kernel full-width half maximum (FWHM) of 2.5 voxel widths = 0.40 mm) using a multithreaded version of csurf wmfilter. Since this method only smooths in directions of low variance and since it is a 2D instead of a 3D operation, it blurs the high contrast boundaries of planar structures much less (Fig. 1, bottom left) than would a 3D Gaussian convolution with a similar FWHM.
Note that, in contrast to the situation with in vivo T1-weighted scans of the neocortex, where the gray/white matter border is characterized by substantial image contrast, the border between the ex vivo cerebellar white matter and the cerebellar molecular layer in our contrastinverted T2*/PD-weighted scans has lower image contrast than the granule cell/molecular layer boundary (i.e., the location of the Purkinje cell layer). Another difference is that the gray/white matter border in the cerebellum approaches itself much more closely than does the neocortical gray/white matter border. Therefore, to obtain the most reliable initial 'white matter' segmentation (wm.mgz), we set the threshold for 'white matter' high enough so that it included the granule cell layer.
The segmented image was then filled (using csurf fill) by recursive region-growing (inside-out, outside-in, and inside-out) to generate a topologically nearly correct block of 'white 6 matter' voxels (filled.mgz). That 'white matter' image was then tessellated (using csurf surf, at native 190 micron wide resolution) to generate an initial surface estimate.
However, numerous small topological defects remained (e.g., "wormholes" connecting adjacent folia or opposite sides of the same folium). The 'white matter' image (wm.mgz) was therefore repeatedly hand-edited, re-filled, and re-tessellated to remove these defects to permit the surface to be unfolded. The resulting surface (4.6M vertices, 9.2M triangles, 25x data size of standard FreeSurfer neocortical hemisphere) was then unfolded (FreeSurfer 5.3 mris_inflate, with non-standard parameters [see csurf Expert Preferences] to accommodate the denser tessellation and larger amount of intrinsic curvature in the cerebellum) (2). See SI Appendix, Figure S2 for a representation of the density of the surface mesh.
The initial folded surface estimate, roughly at the level of the Purkinje cell layer, was also transformed into a gray/white matter surface and a pial surface (Fig. 1, bottom right, yellow and green lines, and Fig. 3) using csurf tksurfer by setting the image criterion for zero image error either to a value just below the brightness of the white matter, or to a low value in order to cause the surface to settle near the pial surface, while including a vertexwise test that prevents surface self-intersection of the estimated surfaces of the tightly packed folia. The non-self-intersecting pial surface estimate was then further refined using the PD scan (csurf tksurfer). Finally, the surfaces were scaled to actual size (0.50/0.19 = 0.38 linear scale factor).
The surface was then cut into pieces (using csurf tksurfer) to allow it to be flattened without severe areal distortion using FreeSurfer 5.3 mris_flatten (3). The flattened representations were used for display purposes (but not areal measurements).

Measurement of area.
Areal measurements are the sum of 'vertexwise area', which is calculated as the sum of 1/3 of the area of each surrounding triangular face of the cerebellar cortex. The surface was first corrected for shrinkage (see below). The surface regions covering the cut peduncles as well as small patches of bare white matter were excluded from the area sum. Those cuts were done on the inflated surface using the curvature coloring to indicate the folia ends, and then the cuts were transferred to the corresponding vertices on the pial surface (csurf tksurfer). 7 The pial surface was chosen for areal measurement because the pial surface has the highest contrast, making it the most definitive measurement. Also, it allowed direct comparisons to previous stereological estimates in the literature.
To make a direct comparison to the in vivo human data for the neocortex, we needed an estimate of the human neocortical pial surface area. This surface is routinely reconstructed in FreeSurfer with the recon-all pipeline. Using FreeSurfer 5.3 reconstructed human scans from our laboratory, the ratio in the neocortex between the gray/white surface area and the pial surface area was measured to be 1.21 (across 32 hemispheres). We therefore multiplied the average female standard "white" surface area taken from the literature by this factor before comparing it to our cerebellar pial surface area.
Correction for shrinkage due to fixation. From a careful longitudinal study of a single human head specimen (4), the brain was found to rapidly expand by about 5% in volume upon removing it from the skull (and being post-fixed for one day in formalin). Then, over a period of 70 days (comparable to the fixation time of our specimen before scanning), the brain volume reached an asymptote of about 8% volume shrinkage compared to the first out-of-skull measurement. This is comparable to the 5-10% volume shrinkage estimates from many previous studies of initial outof-skull volume to final post-fixed volume. Note that this means that the total shrinkage with respect to the in vivo condition is only about 3%. We did not have access to an in vivo scan of the brain of our specimen. However, if we assume an isotropic volume shrinkage of 3% for our specimen (from in vivo to post-fixed ex vivo conditions, equivalent to a ~1% shrinkage in linear dimensions), this will result in a ~2% underestimate of the surface area of the cerebellar pial surface. Before shrinkage correction, the area of the pial surface (minus surface regions covering bare white matter) was 1559 cm 2 . After applying a linear scale factor of 1.01 to the 3D pial surface (3% increase in volume of cerebellar convex hull), we measured a final shrinkagecorrected cerebellar pial surface area of 1590 cm 2 .
We applied the same correction for fixation-induced shrinkage to the cerebellar and neocortical areal estimates for the ex vivo macaque monkey surfaces. 8 Sample cerebellum size in relation to average human cerebellum. Two methods were used to estimate the size of our ex vivo specimen relative to an average human cerebellum.
First, we extracted the left and right cerebellar gray and white matter from the FreeSurfer fsaverage Destrieux atlas volume segmentation (aparc.a2009s+aseg.mgz). The protruding cerebellar peduncles were edited to be flush with the anterior-and superior-most extent of the cerebellar gray matter. The almost-flush peduncle cuts in our specimen were then touched up to match those fsaverage edits. The respective extracted volumes were as follows: fsaverage overall cerebellum volume male+female: 153 cm 3 , our female specimen: 142 cm 3 . After 3% volume shrinkage correction, the surface area of our specimen was 146 cm 3 . This measurement does not rely on the details of image contrast, since the cerebellar convex hull has excellent contrast in both in vivo and ex vivo cases. This is comparable to other slightly differently bounded measurements in the literature (e.g., 134 cm 3 from (6)).
Second, we started with the estimate of the volume of the cerebellar gray matter from (5), which was 118.9 cm 3 for male participants and 109.3 cm 3 for female participants. These volumes are comparable to previous reported volumes of 112 cm 3 (7) and 108 cm 3 (for a group of female participants (8). Applying similar methods to a downsampled version of our data set yielded 118.5 cm 3 . Note that these results have to be treated with some caution, as it is difficult to directly compare in vivo to ex vivo measurements of cerebellar cortical volume given differences in mechanisms of in vivo and ex vivo image contrast, and because the contrast differences have the potential to differentially affect voxel classification. Furthermore, the relatively low resolution used in (6) cannot resolve the extremely tight folding pattern of the folia --therefore the small branches of the white matter embedded in gray matter were not removed.
Overall, however, these two methods suggest that the volume of our human cerebellum specimen is not at all untypical.
For comparison with the human data and with average monkey data, our shrinkagecorrected macaque monkey cerebellum specimen had a volume of 7.36 cm 3 , which was comparable to estimates in the literature, e.g., 7.1 cm 3 in (5).

9
Maximum voxel size capable of full recovery of cerebellar folia in humans. To determine this, we started with the final normalized, contrast-inverted T2*-divided-by-PD 3D data set and then downsampled it, using cubic interpolation, with AFNI 3dresample. We then used the resulting images to re-reconstruct the surface at a variety of downsampled resolutions. There remained a number of tiny topological defects (small 'wormholes' bridging folia) in the reconstructed surfaces which we didn't manually correct since we didn't need to unfold the surface. These are unlikely to have substantially changed the surface area estimate since they often involve only one misclassified voxel, and since the resulting 'wormhole' is stretched into an extremely narrow strand with a much reduced surface area after the surface has been refined. A selection of the downsampling results were as follows: Completeness of recovery of folia from macaque monkey scan. The cerebellar folia of the macaque monkey cerebellum are about one-third the width of the cerebellar folia in humans; but the voxel volume of the macaque monkey scan could only reduced by one-half (0.19 mm to 0.15 mm voxel width) in the present study. On the positive side, the macaque monkey cerebellum reconstruction was less computationally challenging than for the human cerebellum because the branching pattern of the folia in monkeys is much simpler. A main white matter strand emanating from the central white matter core typically branches just a few times in the macaque monkey cerebellum; in humans, by contrast, one main white matter strand may branch into 50 or 60 folia in crus I and II. Accurate initial recovery of the surface of all folia depends upon the FreeSurfer region-growing method (csurf fill) sequentially finding its way throughout every branch in the white matter tree without failures or 'leaks', which are much more likely in the human case, making the monkey cerebellum reconstruction somewhat less susceptible to non-optimal voxel size.
We inspected of every slice image intersected with the final surface reconstruction, to verify that we had in fact recovered every folium, hand-edited the few that were missed, and rereconstructed the surface before measuring its area.
Nevertheless, given the suboptimal ratio between folia width and voxel size in the current macaque monkey data set, it is likely that the surface area of the macaque monkey cerebellum was slightly underestimated. A future study with even smaller voxels will be required to definitively address this question.